We investigate the existence of dS vacua in supersymmetry-breaking Scherk-Schwarz toroidal compactifications of type II string theory, using the well-understood ingredients of curvature, fluxes and 1-loop Casimir energy. Starting from the 10d equations, we derive a series of no-go theorems and existence conditions for dS, and present two explicit, fully-backreacted, solutions: a dS one, which turns out to be not under control, and an AdS one, which can be chosen at arbitrarily weak coupling and large volume by dialling the unbounded fluxes. We then use a lower-dimensional EFT description to show that any dS solution has a universal tachyon and no parametric control. The simplest AdS solutions are also perturbatively unstable. We extend the no-go theorems to slow-roll acceleration and test various swampland conjectures in our non-supersymmetric string setup. The question of numerically controlled, unstable dS is left open.

United Kingdom

Susha Parameswaran

Marco Serra

On (A)dS solutions from Scherk-Schwarz orbifolds

We explore the possibility that our universe’s current accelerated expansion is explained by a quintessence model with an exponential scalar potential, $\textit{V}$ = $\textit{V}$ $\textit{e}$ , keeping an eye towards $\textit{λ}$ ≥ $$ \sqrt{2} $$ and an open universe, favorable to a string theory realisation and with no cosmological horizon. We work out the full cosmology of the model, including matter, radiation, and optionally negative spatial curvature, for all $\textit{λ}$ > 0, performing an extensive analysis of the dynamical system and its phase space. The minimal physical requirements of a past epoch of radiation domination and an accelerated expansion today lead to an upper bound $\textit{λ}$ ≲ $$ \sqrt{3} $$ , which is driven slightly up in the presence of observationally allowed spatial curvature. Cosmological solutions start universally in a kination epoch, go through radiation and matter dominated phases and enter an epoch of acceleration, which is only transient for $\textit{λ}$ > $$ \sqrt{2} $$ . Field distances traversed between BBN and today are sub-Planckian. We discuss possible string theory origins and phenomenological challenges, such as time variation of fundamental constants. We provide theoretical predictions for the model parameters to be fitted to data, most notably the varying dark energy equation of state parameter, in light of recent results from DES-Y5 and DESI.

France

David Andriot

Dimitrios Tsimpis

United States

Timm Wrase

Ivonne Zavala

Exponential quintessence: curved, steep and stringy?

We analyze theories that do not have a de Sitter vacuum and cannot lead to slow-roll quintessence, but which nevertheless support a transient era of accelerated cosmological expansion due to interactions between a scalar <math><mrow><mi>ϕ</mi></mrow></math> and either a hidden sector thermal bath, which evolves as dark radiation, or an extremely light component of dark matter. We show that simple models can explain the present-day dark energy of the Universe consistently with current observations. This is possible both when <math><mi>ϕ</mi></math>’s potential has a hilltop form and when it has a steep exponential runaway, as might naturally arise from string theory. We also discuss a related theory of multifield quintessence, in which <math><mi>ϕ</mi></math> is coupled to a sector that sources a subdominant component of dark energy, which overcomes many of the challenges of slow-roll quintessence.

Joaquim M. Gomes

Edward Hardy

Dark energy with the help of interacting dark sectors

We consider various string-loop, warping and curvature corrections that are expected to appear in type IIB moduli stabilisation scenarios. It has recently been argued, in the context of strongly-warped LVS de Sitter vacua, that it is impossible to achieve parametric suppression in all of these corrections simultaneously [1]. We investigate corrections in the context of the recently discovered weakly-warped LVS de Sitter vacua, which represent a distinct branch of solutions in type IIB flux compactifications. The weakly-warped solution is supported by small conifold flux numbers MK ≲ 32, but still requires a large flux contribution to the D3-tadpole, now from the bulk. Warping corrections become less problematic, and some corrections even help to reach the weakly-warped regime of parameter space. Other corrections continue to be dangerous and would require numerical coefficients to be computed — and found to be small — in order not to destroy the consistency of the weakly-warped LVS de Sitter solution. We motivate why this may be possible.

Bruno Bento

India

Dibya Chakraborty

De Sitter vacua — when are ‘subleading corrections’ really subleading?

We study the gravitational signatures that arise from compactifying Type IIB supergravity on a compact space containing a Klebanov-Strassler warped throat. After reviewing the dimensional reduction of the 10d graviton and explicitly obtaining the equa- tions of motion for the 4d tensor h  μν , vector h  μn  and scalar h  mn  modes, we find the masses and wavefunctions of the Kaluza-Klein tower of spin-2 states. We explore how the masses and wavefunctions depend on the balance between the strength of the warping and the size of the bulk, and how these relate to the range and strength of the interactions which correct the Newtonian gravitational potential. By computing the modified Newtonian potential for sources on a brane somewhere along the throat, and applying consistency constraints on the Klebanov-Strassler parameters, we obtain predictions for the phenomenological pa- rameter space. In the case of a fully warped throat, and depending on where the brane is along the throat, these predictions are narrow in range and consistent with current obser- vational and experimental constraints. We also begin an exploration of gravitational wave signatures of KK gravitons in warped throats, finding that strong warping can bring the corresponding frequencies down to the windows of current and proposed experiments.

Mexico

Gravity at the tip of the throat

In this article we show that finite perturbative corrections in non-supersymmetric strings can be understood via an interplay between modular invariance and misaligned supersymmetry. While modular invariance is known to be crucial in closed-string models, its presence and role for open strings is more subtle. Nevertheless, we argue that it leads to cancellations in physical quantities such as the one-loop cosmological constant and prevents them from diverging. In particular, we show that if the sector-averaged number of states does not grow exponentially, as predicted by misaligned supersymmetry, all exponential divergences in the one-loop cosmological constant cancel out as well. To account for the absence of power-law divergences, instead, we need to resort to the modular structure of the partition function. We finally comment on the presence of misaligned supersymmetry in the known 10-dimensional tachyon-free non-supersymmetric string theories.

Germany

Austria

Niccolò Cribiori

Flavio Tonioni

Modular invariance, misalignment and finiteness in non-supersymmetric strings

We revisit moduli stabilisation for type IIB flux compactifications that include a warped throat region corresponding to a warped deformed conifold, with an anti-D3-brane sitting at its tip. The warping induces a coupling between the conifold’s deformation modulus and the bulk volume modulus in the Kähler potential. Previous works have studied the scalar potential assuming a strong warping such that this coupling term dominates, and found that the anti-D3-brane uplift may destabilise the conifold modulus and/or volume modulus, unless flux numbers within the throat are large, which makes tadpole cancellation a challenge. We explore the regime of parameter space corresponding to a weakly-but-still warped throat, such that the coupling between the conifold and volume moduli is subdominant. We thus discover a new metastable de Sitter solution within the four-dimensional effective field theory. We discuss the position of this de Sitter vacuum in the string theory landscape and swampland.

A new de Sitter solution with a weakly warped deformed conifold

The study of non-supersymmetric string theories is shedding light on an important corner of the string landscape and might ultimately explain why, so far, we did not observe supersymmetry in our universe. We review how misaligned supersymmetry in closed-string theories leads to a cancellation between bosons and fermions even in non-supersymmetric string theories. We then show that the same cancellation takes place for open strings by studying an anti-Dp-brane placed on top of an Op-plane in type II string theory. Misaligned supersymmetry consists in cancellations between bosons and fermions at different energy levels, in such a way that the averaged number of states grows at a rate dominated by a factor   <math> <msup> <mi>e</mi> <mrow> <msub> <mi>C</mi> <mi>eff</mi> </msub> <msqrt> <mi>n</mi> </msqrt> </mrow> </msup> </math>  $$ {\mathrm{e}}^{C_{\mathrm{e}\mathrm{ff}}\sqrt{n}} $$ , with C eff &lt; C tot, where C tot is the inverse Hagedorn temperature. We prove the previously conjectured complete cancellation, i.e. we prove that C eff = 0, for a vast class of models.

Misaligned supersymmetry and open strings

This article discusses model-building scenarios including anti-D3-/D7-branes, in which supersymmetry is broken spontaneously, despite having no scale at which sparticles appear and standard supersymmetry is restored. If the branes are placed on singularities at the tip of warped throats in Calabi-Yau orientifold flux compactifications, they may give rise to realistic particle spectra, closed- and open-string moduli stabilisation with a Minkowski/de Sitter uplift, and a geometrical origin for the scale hierarchies. The paper derives the low-energy effective field theory description for such scenarios, i.e. a non-linear supergravity theory for standard and constrained supermultiplets, including soft supersymmetry-breaking matter couplings. The effect of closed-string moduli stabilisation on the open-string matter sector is worked out, incorporating non-perturbative and perturbative effects, and the mass and coupling hierarchies are computed with a view towards phenomenology.

Non-supersymmetric string models from anti-D3-/D7-branes in strongly warped throats

We present a novel source of dark energy, which is motivated by the prevalence of hidden sectors in string theory models and is consistent with all of the proposed swampland conjectures. Thermal effects hold a light hidden sector scalar at a point in field space that is not a minimum of its zero temperature potential. This leads to an effective “cosmological constant,” with an equation of state <math><mi>w</mi><mo>=</mo><mo>−</mo><mn>1</mn></math>, despite the scalar’s zero temperature potential having only a four-dimensional Minkowski or anti–de Sitter vacuum. For scalar masses <math><mrow><mo>≲</mo><mi>μ</mi><mi>eV</mi></mrow></math>, which could be technically natural via sequestering, there are large regions of phenomenologically viable parameter space such that the induced vacuum energy matches the measured dark energy density. Additionally, in many models a standard cosmological history automatically leads to the scalar having the required initial conditions. We study the possible observational signals of such a model, including at fifth force experiments and through <math><mi>Δ</mi><msub><mi>N</mi><mi>eff</mi></msub></math> measurements. Similar dynamics that are active at earlier times could resolve the tension between different measurements of <math><msub><mi>H</mi><mn>0</mn></msub></math> and can lead to a detectable stochastic gravitational wave background.